Step-by-step explanation:
x = Alice's money
y = Mio's money
z = Grace's money
x + y + z = sum
there are originality 5+4+3 = 12 parts of the money shared between them.
x = 5/12 sum
y = 4/12 sum
z = 3/12 sum
after the money transfer we are only having 4+3+2 = 9 parts of the same money distributed.
so, we are dealing with 1/9 parts.
let's bring everything to 1/36 to be able to truly compare things.
therefore
x = 15/36 sum
y = 12/36 sum
z = 9/36 sum
15/36 sum + 10 = 16/36 sum
because 4/9 = 16/36
10 = 1/36 sum
sum = 10×36 = £360
so, together they have £360.
and they had before the £10 transfer £150, £120, £90.
after the £10 transfer they had £160, £120, £80.
Answer:
1) By SAS theorem, ΔADE≅ΔCDF
2) By SSS theorem, ΔBDE≅ΔBDF
Step-by-step explanation:
Consider isosceles triangle ABC (see diagram).
1. In triangles ADE and CDF:
- AD≅DC (since BD is median, then it divides side AC in two congruent parts);
- AE≅CF (given);
- ∠A≅∠C (triangle ABC is isosceles, then angles adjacent to the base are congruent).
By SAS theorem, ΔADE≅ΔCDF.
2. In triangles BDE and BDF:
- side BD is common;
- DE≅DF (ΔADE≅ΔCDF, then congruent triangles have congruent corresponding sides);
- BE≅FB (triangle ABC is isosceles, AB≅BC, AE≅CF, then BE=AB-AE, FB=BC-CF).
Be SSS theorem, ΔBDE≅ΔBDF.
Answer:
(-1/2,-5/2)
Step-by-step explanation:
x-y = 2
x+y = -3
---------------
Through Elimination, we can just add the system of equations. The y cancels out and gives us the single equation for x:
2x = -1
x = -1/2
Substitute -1/2 for x in either equation and you get:
(-1/2) + y = -3 Solve for y
y = -5/2
--------------
Step-by-step explanation:
The position of the mouse at time t is 4 + 12t.
The position of the cat at time t is 17t.
When the positions are equal:
4 + 12t = 17t
4 = 5t
t = 0.8
It takes 0.8 seconds.
They want to know the area of the letters that are besides it or they want or know what points they are at.
